Formation of precipitates in off-stoichiometric Ni–Mn–Sn Heusler alloys probed through the induced Sn-moment

The shell-ferromagnetic effect originates from the segregation process in off-stoichiometric Ni–Mn-based Heusler alloys. In this work, we investigate the precipitation process of L21-ordered Ni2MnSn and L10-ordered NiMn in off-stoichiometric Ni50Mn45Sn5 during temper annealing, by X-ray diffraction (XRD) and 119Sn Mössbauer spectroscopy. While XRD probes long-range ordering of the lattice structure, Mössbauer spectroscopy probes nearest–neighbour interactions, reflected in the induced Sn magnetic moment. As shown in this work, the induced magnetic Sn moment can be used as a detector for microscopic structural changes and is, therefore, a powerful tool for investigating the formation of nano-precipitates. Similar research can be performed in the future, for example, on different pinning type magnets like Sm-Co or Nd-Fe-B.


Introduction
Due to the multifaceted phase diagram 1,2 of magnetic Heusler alloys, this material class possesses a variety of interesting phenomena. 3 For example, NiMn-Heusler alloys show a magnetostructural phase transition 4 or intrinsic exchange bias 5 due to the presence of mixed magnetic interactions (antiferromagnetic and ferromagnetic). [6][7][8][9][10] Besides, it shows the possibility of adjusting the magnetic anisotropy energy, e.g. by interstitial doping 11 and, therefore, serves as a prototype system for investigations of fundamental physical phenomena such as structural disorder. 12 These properties make Heusler alloys interesting for serveral applications, for example, in the area of magnetic shape-memory, 13 magnetocalorics 14 and spintronics. 15 Heusler alloys have a huge potential for applications, however, off-stoichiometric variations of Heusler alloys suffer due to a tendency of segregation. Sokolovskiy et al. 10 recently performed DFT-calculations and showed that off-stoichiometric Mn-rich Ni 2 Mn 1+x (In,Sn,Al) 1−x compounds are unstable at low temperatures and decompose into a dual phase system. However, it is possible to utilize this process, as it will be discussed in the following. The shell-ferromagnetic effect is a newly achieved property of the off-stoichiometric Heusler compound, which is less well studied and occurs in Mn-rich antiferromagnetic (AF) Heusler-based compounds 16 and opens paths to different functionalities. This effect occurs when Ni 50 Mn 45 Z 5 (Z: Al, Ga, In, Sn, Sb) decomposes into cubic L2 1 ferromagnetic (FM) Heusler Ni 50 Mn 25 Z 25 and L1 0 -ordered AF Ni 50 Mn 50 during temper-annealing at temperatures around 600 K < T A < 750 K, where T A is the annealing temperature. By applying a magnetic eld during the annealing process, nanoprecipitates are formed within a strongly pinning AF matrix, originating from Ni-Mn and off-stoichiometric Ni 50 Mn 45 Z 5 . A collection of these nano precipitates in a macroscopic sample gives rise to a partially compensated magnetic response to an applied magnetic eld, which has been demonstrated in a video. 17 The observed pinning mechanism implies that the formed precipitates could form building blocks for highperformance and lightweight permanent magnets of unsurpassed coercivity. The magnetic moment at the interface of Ni-Mn and Ni 2 MnSn, becomes pinned in the direction of the applied magnetic eld during annealing so that the elddependence up to 9 T appears as a vertically shied hysteresis loop, while it is a minor loop within a major loop with a coercive eld exceeding 5 T. 18 The remanent magnetisation of the loop is always positive and only reorientates entirely in elds exceeding 20 T (T < 550 K). The core structure of the precipitate (Ni 2 MnZ) is, however, magnetically so, and the spins rotate freely in the direction of an applied magnetic eld. These structures were rst found as a result of decomposing Ni 50 Mn 45 In 5 (ref. 19) or Ni 50 Mn 45 Ga 5 (ref. 16) at 650 K in a magnetic eld. For the effective compensation of the magnetisation, the surface-to-volume ratio of the precipitate is important. For the case of a large surface-to-volume ratio, the magnetisation of the Ni 2 MnZ-nano-precipitates can be compensated by the Ni-Mn surrounding. For larger Ni 2 MnZ-precipitates, the Ni-Mnsurrounding is not sufficient for the compensation of Ni 2 MnZ spins, and the shell-ferromagnetic effect does not occur. Scherrer analysis indicates a precipitate size of 3-5 nm for Ni 50 Mn 45 In 5 annealed at 650 K, corresponding to a surface-tovolume ratio 20 of 1.2-2 nm −1 , while for Ni 50 Mn 45 Sb 5 the precipitate size is in a similar range of 5-10 nm. 21 Besides the potential use case in permanent magnets, these magnetically pinned precipitates can be used in materials possessing a rstorder magnetostructural phase transition, 22 where the precipitates may serve as a nucleation site for the phase transition. In this case, the precipitates may induce a local strain eld that can energetically favour the martensite-austenite transition. This mechanism has the potential to improve magnetocaloric properties 23,24 of this compound or can increase the mechanical stability. [25][26][27][28][29][30] Within the current work, we report on our recent ndings characterising Ni-Mn-Sn precipitates and show that 119 Sn-Mössbauer spectroscopy is an ideal technique to study the precipitate formation due to the possibility to probe nearestneighbour interactions through the Sn nuclei. Therefore, we can observe phases with a short-range ordering otherwise absent or difficult to detect with XRD. We will show this trend by comparing our spectroscopic insights with X-ray diffraction results that resolve long-ranged ordering. 119 Sn-Mössbauer spectroscopy tracks the formation of stoichiometric Ni 2 MnSn clusters inside an antiferromagnetic Ni 50 Mn 45 Sn 5 matrix for mild annealing temperatures. Here, we indirectly probe the induced Sn-moment and use this spectroscopic feature as a detector for the structural transition, without the need for another tracing dopant used for example in ref. 31, which leads to local distortions and effects the physical properties. On the other hand, X-ray diffraction is a well-known and effective tool to probe the long-range ordering of the whole sample volume.

Results & discussion
In order to test the sensitivity of the Sn hyperne eld to structural changes, we performed 119 Sn-Mössbauer spectroscopy at room temperature on the AFM-ordered off stoichiometric L1 0 -alloy Ni 50 Mn 45 Sn 5 and stoichiometric FM-ordered L2 1 Ni 2 MnSn alloy (see Fig. 1(a) & (e)). 32 The magnetic ordering of the samples leads to the liing of the degeneracy of the 119 Sn hyperne levels and the occurrence of a sextet structure. In the following both spectra are described by a hyperne eld distribution p(B Sn hf ) which is (shown in Fig. 1(f) & (j)) for the L1 0 and L2 1 -ordered alloy, respectively. The spectrum of the L1 0 -ordered alloy (see Fig. 1(a)) possesses a relatively broad hyperne eld distribution ranging from 0 T to almost 28 T (see Fig. 1(f)) with an average hyperne eld hB Sn hf i of 12.1 T. The broad distribution of hyperne elds indicates different local surroundings around the 119 Sn-nuclei. In contrast, the L2 1 -ordered alloy feature a smaller distribution with distinct ne structure at 2 and 6 T leading to an average hyperne eld hB Sn hf i of 3.9 T. The present distribution of hyperne elds indicates the presence of structural or magnetic disorder and expresses small variations from the L2 1 -crystal structure, since for the L2 1 structure, we would assume the presence of a single Sn-environment leading also to a single spectral contribution. This phenomenon has been extensively discussed in a recent work on the effect of magnetic and anti-site disorder for the Snpartial phonon density of states in Ni 2 MnSn, 33 and goes beyond the scope of the current work. These defects could be present in the form of anti-site disorder between Mn and Sn atoms caused due to the slight deviation of the perfect 2-1-1 stoichiometry (see Table 2). By comparing these two compositions, we can conclude that replacing Mn with Sn dilutes the absolute magnetic moment and, therefore, reduces the 119 Sn hyperne eld. Accordingly, the major contribution in the hyperne eld distribution (see Fig. 1(f) & (j)) shis towards smaller elds and reects the decreased Sn moment. Here, we cannot determine the exact change of the Sn magnetic moment due to the complex relationship between the magnetic moment and the hyperne eld. For Sn, the proportionality constant A between the Sn moment m Sn and the Sn hyperne eld B Sn hf depends on different materials properties, e.g. the anisotropy of the system. [34][35][36] Furthermore, the effective hyperne eld measured at the 119 Sn nucleus is composed of several terms. There are direct (dipolar) and indirect (transfered hyperne eld from neighboring atom to 119 Sn nucleus) terms. There is also the possibility that the Sn atom is itself polarized from its surroundings and generates a direct (contact) hyperne eld. Without further information (for example XMCD spectra of Sn), we can only conclude that the measured B Sn hf is the sum of relevant contributions. Therefore, the determination of the magnetic Sn-moment m Sn is beyond the scope of this work.
In the following, the decomposition process will be investigated. As stated in previous investigations, 16,19,20 the decomposition process in the off-stoichiometric Heusler compound follows the route In the following, we assume that for nite annealing times, the overall decomposition process can be described with an additional residual component, leading to a modication of eqn (1) to Ni 50 Mn 45 Sn 5 /ð1 À x À y À zÞ$Ni 50 Mn 45 Sn 5 þ x$Ni 2 MnSn þ y$NiMn þ z$ X r;k;3 p r;k;3 $Ni r Mn k Sn 3 ; where Ni r Mn k Sn 3 is the residual Sn-containing phase with unknown stoichiometry, while x, y, z, and p r,k,3 is the respective molar fraction of the respective phase. Due to excitation of the nuclear resonance, 119 Sn-Mössbauer spectroscopy probes only Sn-containing phases. Therefore, in the discussed case, one can track the temporal evolution of the decomposition process by identifying spectral ngerprints for the respective Sn-containing phases. Based on eqn (2), it is possible to probe the initial compound Ni 50 Mn 45 Sn 5 , the Ni 2 MnSn-core structure, and the Sn-containing residual phase Ni r Mn k Sn 3 , while the formation of Ni-Mn can not be observed via 119 Sn-Mössbauer spectroscopy, due to the missing Sncontent. With the spectral ngerprint of the initial and the core-precipitate compound (see Fig. 1(a) & (e)) the experimental spectra of the decomposed state can be described by a leastsquares tting routine, assuming a superposition of the known theoretical models (for Ni 50 Mn 45 Sn 5 and Ni 2 MnSn), while an additional hyperne eld distribution p(B Sn hf ) describes the residual spectral contributions arising from unknown compositions. Based on this model, we can model the 119 Sn Mössbauer spectra for annealing times t A of 3 h, 17 h, and 200 h (see Fig. 1(b)-(e)), while Fig. 1(g)-(i) depicts the obtained hyperne eld distributions and the overall sum. Here the annealing temperature T A was chosen to be 650 K, since at these temperatures similar studies on Ni 50 Mn 45 In 5 (ref. 20) or Ni 50 Mn 45 Sb 5 (ref. 21) indicate that the size of the precipitate is almost temperature independent and below 10 nmresulting in a sizeable surface-to-volume ratio. The size of the precipitates leads to the intrinsic compensation of the respective magnetic moments in the Ni-Mn shell and Ni 2 MnSn coreresulting in the shell-ferromagnetic effect 19 and the occurrence of these large coercivity elds. 18 The comparison of the hyperne eld distributions reveals the shi of the maximum hyperne eld towards smaller values with increasing annealing times t A , while aer annealing for 200 h, the majority of the hyperne eld contribution originates from stoichiometric Ni 2 MnSn. The relative spectral area (see Table 1) supports this trend: with increasing annealing duration, the Ni 2 MnSn and residual contribution increase. Here, we want to mention two further aspects. Our room temperature measurements do not indicate a signicant contribution of superparamagnetic Ni 2 MnSnclusters, since we only observe a minor contributions at low hyperne elds in the residual phase. On the other hand, measurements performed above the Curie temperature of Ni 2 MnSn (not shown here) show similar spectral contributions to the previously discussed room temperature measurements, but show a major singlet contribution, indicating the collapse of long-range magnetic ordering.
X-ray diffraction probes the long-range ordering of the lattice structure. Fig. 2 depicts the X-ray diffractograms for the decomposed states aer 3, 17, and 200 h for annealing temperature T A of 650 K. In contrast to the spectroscopy, XRD measurements have been performed on bulk ingots, while aer annealing the surface has been polished. Due to the present texture of the sample and the relative small grain size of the Ni 2 MnSn-precipitates, 20,21 the (110) and (200) superlattice peaks of the L2 1 structure possess a small intensity. These diffractograms indicate that Ni 50 Mn 45 Sn 5 crystallizes in its initial L1 0 -phase, similar to Ni-Mn with a small deviation of the lattice constant, while the stoichiometric compound Ni 2 MnSn possess a L2 1 ordering. Only aer annealing the sample for 200 h, the decomposition becomes visible in the XRD-pattern as a splitting of the (110) L1 0 -peaks. Additional detailed analysis shows that the (004) and (224) peaks of the L2 1 full Heusler Ni 2 MnSn alloy are barely visible aer annealing for 200 h. The small contribution of the L2 1 -phase in the XRD pattern can be explained by the relatively small precipitate size 20,21 (below 10 nm) and the low phase fraction of the formed full-Heusler precipitates. For the investigated post-annealing conditions, the XRD patterns indicate that the long-range ordering of the sample has barely changed, while Mössbauer spectroscopy reveals drastic variations of the Sn nearest neighbour surrounding. These variations of the local surrounding are reected in the nuclear hyperne levels.

Summary
Within this work, we investigated the formation of Ni 2 MnSnprecipitates in off-stoichiometric Ni 50 Mn 45 Sn 5 via X-ray diffraction and Mössbauer spectroscopy. Here, the transferred hyperne eld (or the induced magnetic moment) of 119 Sn is an interesting property for investigating and tracking the precipitation process. While X-ray diffraction reveals long-range ordering, 119 Sn-Mössbauer spectroscopy probes nearest-neighbour interactions and is, therefore, especially sensitive to changes in the local surrounding. Due to these differences in the probed length scale, we can explain the different occurring dynamics. Employing extended X-ray absorption ne structure (EXAFS) spectroscopy, this concept can be adapted to different material systems. For example, one can probe the diffusion at grain boundaries 37 in Nd 2 Fe 14 B or Sm-Co, 38 or one can use scanning transmission X-ray microscopy 39 and nd  a connection between the local structure and high coercivity occurring in high-performance permanent magnets.

Experimental details
All samples were prepared by arc melting of pure elements (Ni: 99.98%, Mn: 99.99%, Sn: 99.999%). Aerwards, the obtained material was encapsulated in a quartz tube under argon atmosphere and homogenized for ve days at 1073 K, followed by quenching in room temperature water and polished. Energydispersive X-ray spectroscopy inside a scanning electron microscope veries the composition of the prepared alloys (see Table 2). X-Ray diffraction measurements were performed on a polycrystalline bulk ingot using a Phillips PANalytical X'Pert PRO with non-monochromatized X-rays (Cu X-ray source) in a Bragg-Brentano geometry, and the obtained diffraction patterns were analyzed using JANA2006. 40 For the investigation of the decomposition, Ni 50 Mn 45 Sn 5 was annealed a temperature of 650 K for different times under high vacuum conditions (p z 5 × 10 −5 mbar) to avoid oxidation of the sample. During the annealing process, no magnetic eld has been applied. Room temperature 119 Sn-Mössbauer spectroscopy measurements were performed in transmission geometry under zero-eld conditions with conventional electronics. The velocity of a Ca 119 SnO 3 source was changed within the constantacceleration mode and calibrated with a laser interferometer. The experimental spectra have been evaluated by a least-squares tting routine using the Pi program package. 41

Conflicts of interest
There are no conicts to declare.